A hardware wallet that connects to an internet connected device directly is itself connected to the internet.
Not at all, in my opinion. What you say implies that basically every hardware wallet would be connected to the internet, which is wrong.
I'm not trying to convince you, we both likely have a different interpretation of this matter. I'll just say this: if a hardware wallet's firmware and hardware components don't have code or in-built abilities to talk to a network, they're offline to the internet because there's no way the hardware wallet could interact with the network in any case. They can't connect to the internet and vice-versa. Period!
Their whatever connection to a watch-only software wallet part is commonly only used to exchange transaction data which is signed on user's consent by the hardware wallet. The only thing the online watch-only software wallet pulls from the hardware wallet is the signed transaction when the user has agreed to sign it (prior it pushed the unsigned transaction to the hardware wallet).
Usually there's no code in the firmware of a decent and secure hardware wallet that would allow the connected software wallet to pull any of the main secrets which are hopefully or provably kept secure in the hardware wallet, like wallet's initial entropy, derived seed, private keys or extended private keys in the context of BIP32 derivation.
For wallets with open-source firmware, we could check this. For wallets with closed-source firmware we can't. Nothing new on this front.
Second an offline wallet is one that is always offline, otherwise the word offline wallet is meaningless..
A cold wallet is by definition offline and has to stay offline for all time, otherwise it's not a cold wallet anymore. The moment a cold wallet becomes online, it looses its "cold" status forever by definition. Being online, the wallet becomes hot and can't get "cold" anymore.